The item that is no required to complete the game is the apple you need the bean to get to zacks castle and the cow to get the bean the aplle is optional you can either give it to the troll or not not a nessary

Yep, it was a trick question
The answer I was looking for was all of the above; you don't need to give the troll the apple, you can water the manure without the bean, and therefore not need to give the cow to the merchant. That doesn't apply to the Amiga/Atari ST/DOS remakes, though.

Nah, I went back and confirmed this on Atari ST: The troll wouldn't appear in the mine until I gave the troll the apple, and the coin wouldn't appear until I visited the troll in the mine. Even hitting the fire button all around the troll's starting location failed to work until the coin actually appeared.